Compensating Low-Frequency Signals for Prestack Seismic Data and Its Applications in Full-Waveform Inversion

Cycle-skipping problem is one of the major impediments for full-waveform inversion (FWI) to accurately recover subsurface velocity models. The multiscale inversion scheme is a practical and robust strategy to mitigate the cycle-skipping issue. The success of this strategy depends on the existence of low effective frequency components in prestack seismograms. Due to the limited frequency band of the source and receiver, as well as the effects of noises, the low-frequency signals in seismic records are usually either too noisy or totally absent. We explore the possibility of compensating certain low-frequency components for observed band-limited records and apply compensated data to FWI for accurately building subsurface velocity models. We first assume the convolution model holds true for the prestack seismograms, and validate this assumption using a numerical experiment for the Marmousi model. We find that when there are effective low-frequency signals in the records, high-frequency waveforms can be converted to low-frequency waveforms using a deconvolution and convolution filter. However, this strategy fails when the low-frequency signals are missing. Considering the sparsity of seismic wave arrivals, we propose first to estimate Green's function by solving an L-1-norm regularized linear inverse problem, and then construct a new dataset by convolving the estimated Green's function with a new source function with low-frequency components. Numerical examples for 2-D Amoco and Marmousi models show that the low-frequency compensated data are consistent with the reference data that are computed by using a source wavelet with low-frequency components. By incorporating this low-frequency compensation strategy into a traditional multiscale FWI scheme, we design a modified workflow for recovering the subsurface velocity model hierarchically. Numerical experiments demonstrate that the compensated low-frequency information enables us to resolve large-scale velocity perturbations and mitigate the cycle-skipping problem.